Is it permissible to pray for the dead and for children after every prayer at home, as is done in the Two Holy Mosques, and what is the meaning of praying for a child?

Funeral prayers in the Two Holy Mosques are performed for deceased persons who are present before their burial. It is not prescribed to perform them for deceased persons who are not present after every prayer, nor for all Muslim deceased. Repeating them after every prayer for someone who has already been prayed upon is an innovation (bid'ah). A Muslim child is to be prayed upon, and the Prophet, peace and blessings be upon him, commanded to pray upon him, and supplication is made for his parents for forgiveness and mercy. Praying over a child who has not reached puberty is like praying over an adult, and the supplication for him can be the traditional supplication for an adult deceased, with the permissibility of adding to it.